The following line passes through point $(2, 7)$ : $y = \dfrac{8}{7} x + b$ What is the value of the $y$ -intercept $b$ ?
Explanation: Substituting $(2, 7)$ into the equation gives: $7 = \dfrac{8}{7} \cdot 2 + b$ $7 = \dfrac{16}{7} + b$ $b = 7 - \dfrac{16}{7}$ $b = \dfrac{33}{7}$ Plugging in $\dfrac{33}{7}$ for $b$, we get $y = \dfrac{8}{7} x + \dfrac{33}{7}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(2, 7)$